Trade policy and Tari�-jumping FDI when

quality matters

Bénédicte Coestier, Université de Paris Ouest Nanterre La Défense ∗

Draft - August 2009

Résumé

In this paper, we consider a situation where there are two �rms, an

incumbent domestic �rm o�ering a high-quality good and an emerging

multinational o�ering a product of lower quality. We analyse how the

assumption of �xed costs of quality versus variable costs of quality - com-

bined with the hypothesis of price versus quantity competition - a�ects

the optimal trade policy, as well as the emerging multinational incentive

to invest rather than export.

Keywords : Vertical product di�erentiation, Bertrand and Cournot compe-tition, trade policy, FDI

JEL classi�cation numbers : L13, F13.

1 Introduction

Multinationals from emerging and developing countries are increasingly contri-buting to the growth of world foreign direct investment (FDI) �ows. Developingeconomies' outward FDI stocks as a percentage of GDP rose from 3.8% in 1990to 12.2% in 2003. Measured as a share of gross �xed capital formation, somecountries invest more abroad than some developed ones : for example, Singa-pore (36%), Taiwan (10%), Chile (7%) and Malaysia (5%), compared to theUnited States (7%), Germany (4%) and Japan (3%). Others, such as India,China, Brazil, are at the take-o� stage. According to UNCTAD (2004), the top50 multinationals from the South are becoming `transnationalized' at a fasterrate than their developed-country counterparts.

This phenomenon is actually not new. Previous research on the so-called`Third World Multinationals' (Wells, 1983) aimed at identifying their characte-ristics and pattern of FDI. These `emerging multinationals' were usually smaller,more labor-intensive and technology-�exible than the developed-country multi-nationals. Also, their output was generally lower in quality and their competitive

∗Email : coestier@u-paris10.fr

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adavantages were based on price rather than product di�erentiation. They in-vested in neighbouring developing countries where levels of industrialization andtechnological capabilities were lower, but where they would have a competitiveedge over developed countries' �rms due to closer demand conditions betweenhome and host markets. Although this interpretation seems relevant to an ana-lysis of downstream South-South FDI, it appears less relevant for explaining theexistence of upstream South-North FDI, a topic, in fact, little explored.

In the late 1980s, countries such as South Korea and Taiwan, direct investedin a signi�cant manner not only in developing countries but also in developedones, before they were considered to have joined the ranks of industrializednations (Van Hoesel, 1999 ; Sachwald, 2001). More recently, China and SouthAfrica have been also targeting developed-country markets : the US is the seconddestination, after Hong Kong, for Chinese multinationals, and 75% of SouthAfrica's FDI stock is in Western Europe.

A �rst intriguing issue relates to the nature of emerging multinationals' com-petitive advantages, which � according to received foreign investment theory(Caves, 1996) � are a necessary precondition for overcoming entry barriers toforeign markets. Considering that multinationals from the South are unlikely topossess intangible assets in the form of advanced technology or brands, notablyvis-à-vis domestic �rms in the North, they are more likely to target the lower-end segments of developed-country markets rather than focus on di�erentiationthrough quality and innovation. This was the case for Korean multinationals,where their early expansion in the US and EU was not based on R&D or mar-keting advantages, but on producing low cost mature products (Perrin, 2001).

The tari�-jumping motivation is another prospective in�uence to examinewhen one analyzes the growth of South-North FDI. The role of trade barriers'circumvention has been emphasized as a pull factor when it comes to explainingthe remarkable growth of Japanese investment in the US and the EU (Azrak andWynne, 1995 ; Barrel and Pain, 1999 ; Belderbos, 1997). As with the Japanesecase, Korean �rms have been sensitive to developed countries' trade restrictionsand tari�-jumping has been an important determinant of Korean FDI, parti-cularly in the electronics industry (Coestier and Perrin, 2005). This seems tobe a necessary option for strongly export-oriented �rms which are overly de-pendent on world demand, and thus need to protect their market share in caseof trade barriers. Trade frictions between developed and developing countriesare still frequent : e.g. the US and the EU launched, respectively, 42 and 17anti-dumping actions between July 2003 and June 2004, of which 84% and 94%targeted developing and emerging economies. China was the top `o�ender' with19 cases, followed by India, Thailand and South Korea (WTO, 2004). Thus,emerging multinationals facing protectionist threats may well have a strong in-centive to support their exports and expand their market presence by `jumping'trade restraints through international production.

In this paper, we characterize this situation in a simple model with verticalproduct di�erentiation, where there are two �rms, an incumbent domestic �rmo�ering a high-quality good and an emerging multinational o�ering a productof lower quality. In contrast to the pioneering literature on strategic investment

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(Smith, 1987 ; Motta, 1992), which emphasized the entry-deterring nature ofFDI, emerging multinationals' direct investment in developed countries can beseen as a response to trade restraints which threaten to increase costs vis-à-vislocal rivals (tari�-jumping FDI). This follows Belderbos' (1997a) analysis ontari�-jumping FDI in a Cournot setting with homogenous goods.

We analyse how the assumption of �xed costs of quality versus variable costsof quality - combined with the hypothesis of price versus quantity competition -a�ects the optimal trade policy, as well as the emerging multinational incentiveto invest rather than export. Both types of assumptions might be important.Variable costs of quality in contrast to �xed costs are re�ected in market prices.In a context of product di�erentiation, product market competition matters.Under Bertrand competition, �rms compete for the marginal consumer andthe higher the quality di�erential, the higher the pro�ts of both �rms. UnderCournot competition, the pro�t of each �rm increases with its own quality anddecreases with the rival's quality.

The product di�erentiation context we consider to analyse tari�-jumpingFDI has notably been used by the theoretical literature on FDI responses toantidumping actions (cf. Vandenbussche and Wauthy (2001) and Belderbos etal. (2004)). These papers appear as quite speci�c with respect to the assumptionon quality costs : Vandenbussche andWauthy (2001) neglects quality costs whichare set to zero, while Belderbos et al. (2004) consider that the foreign �rm hasa marginal cost advantage.

The paper is organized as follows. In the next section, we present the basicmodel. In section 3, we examine the optimal protection situation when qualitymatters. Section 4 is devoted to the exports vs FDI decision. This is followedby concluding remarks.

2 The model

We consider an industry characterized by vertical product di�erentiation.There are two �rms, the domestic �rm labelled Firm 1 that produces high qua-lity, and the foreign/emerging multinational �rm labelled Firm 2 that produceslow quality. Both �rms sell their products to domestic consumers who are willingto buy one unit at most of the good, and have heterogeneous preferences iden-ti�ed by their taste for quality, θ, which is uniformly distributed on the interval

[θ, θ], with density equal to 1.

The net utility of consuming good i for the consumer with taste θ is

U ={θsi − pi if he buys one unit of the good of quality si at price pi

0 otherwise

where si refers to quality and pi is the unit price of good i. Quality is exogeneousand s1 denotes the high quality and s2 the low quality o�ered in the market

3

(s1 > s2). The consumer who is indi�erent between consuming high, or low,

quality good is identi�ed by the taste parameter

θ̃1 =p1 − p2

s1 − s2assuming p1 > p2. The consumer indi�erent between buying the low qualitygood and not buying at all is identi�ed by the taste parameter

θ̃2 =p2

s2

Consumers described by θ̃2 > θ > θ will not buy at all1. Hence, demandsfor, respectively, the high (s1) and low (s2) quality good are :

x1(p1, p2) = θ − p1 − p2

s1 − s2; x2(p1, p2) =

p1 − p2

s1 − s2− p2

s2(1)

and the respective inverse demands :

p1(x1, x2) = θs1 − x1s1 − x2s2; p2(x1, x2) = (θ − x1 − x2)s2 (2)

Firm i's cost function is :

C(si, xi) = h(si)xi + c(si)

where xi is the output. In the following, we shall consider that the cost ofquality improvement either falls into �xed costs, in which case, h(si) = 0, or intovariable costs, in which case, c(si) = 0. When quality costs are �xed costs, theyare considered as sunk costs in the market competition stage. When the costof quality is variable the quality dimension may refer to the quality of inputs.While when the cost of quality is �xed, the quality dimension rather refer toinnovation.

As noticed above, quality is considered as �xed : the quality choice is notinvestigated. The foreign �rm supplies low quality and the domestic �rm supplieshigh quality which re�ects in the cost structure ; h(s1) > h(s2) and c(s1) >c(s2) so that C(s1, x1) > C(s2, x2) for all x1 = x2. This amounts to considerthat the foreign �rm has a cost advantage over the domestic �rm, linked tothe quality embodied in the product.This assumption is consistent with theresults established by Motta (1993) and Herguera et alii (2002) that productdi�erentiation always arises at equilibrium. We further assume that the foreign�rm's cost advantage is transferable abroad : it incurs the same cost of quality(either �xed or variable) under investment or export.

The decision to invest or export depends on the nature of additional coststhe foreign �rm prefers to avoid. Investment implies an additionnal �xed cost

1We have to assume that the market is not covered for demand functions to be inverted.

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denoted G while it allows to save on exporting costs, that is unit transportcost, d, and potential tari�, t. This �xed cost is di�erent from the �xed costassociated to quality and refers for instance to the setting of a new plant. Notethat given these assumptions, whatever the positive tari� level and whatever theassumption on quality costs, the marginal cost under investment is lower thanthe marginal cost under export. It is less costly, in terms of variable productioncosts, to set up local production to substitute for exports. This is a necessarycondition for the multinational to have incentives to invest rather than exportwhen the government of the potential host country imposes a tari�.

3 Optimal protection when quality matters

In this section, we characterize the optimal protection when goods of di�erentqualities are traded and �rms compete either in quantity or price.

We derive the duopoly equilibrium solutions under each competitive setting,and the socially optimal tari�.

3.1 The Cournot case :

3.1.1 International duopoly : the export case

We consider the situation where Firm 2 chooses to export on the foreignmarket and that the government imposes a tari�, t. We consider ex ante tari�in the sens that the level of policy is chosen by the government before the marketcompetition stage2. The free trade situation is obtained setting t = 0.

The pro�t functions of Firms 1 and 2 are

π1(x1, x2) = (θs1 − x1s1 − x2s2)x1 − h(s1)x1 − c(s1)

π2(x1, x2) = (θ − x1 − x2)s2 x2 − (t+ d+ h(s2))x2 − c(s2)

Both �rms compete to attract consumers. In the Nash equilibrium, each �rmmaximizes its pro�t with respect to quantity, given the quality pair (s1, s2).

Best response functions :

x1(x2) =

{θs1−x2s2−h(s1)

2s1if x2 <

θs1−h(s1)s2

0 otherwise

x2(x1) =

{(θ−x1)s2−h(s2)−(t+d)

2s2if x1 < θ − (t+d+h(s2))

s20 otherwise

2For an analysis of the impact ex-post tari�s on quality choices, cf. Herguera et alii (2002).

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Using the reaction functions, we �nd that quantities are3 :

x1(t) =θ(2s1 − s2) + t+ d+ h(s2)− 2h(s1)

(4s1 − s2)(3)

x2(t) =s1s2

θs2 − 2(t+ d+ h(s2))(4s1 − s2)

+h(s1)

(4s1 − s2)(4)

The higher the marginal cost of the foreign �rm (t + d + h(s2)), the lowerthe output of the foreigh �rm and the higher the output of the domestic �rm.And the foreign �rm output is more sensible to a change in the tari� or in thetransport cost than the domestic output.

These optimal quantities yield the following prices

p1(t) =s1θ(2s1 − s2)

4s1 − s2+s1(t+ d+ 2h(s1) + h(s2))

4s1 − s2− h(s1)s2

4s1 − s2(5)

p2(t) =θs1s2 + (t+ d+ h(s2))(2s1 − s2) + h(s1)s2

(4s1 − s2)(6)

and equilibrium pro�ts,

Π1(t) = p1(t)x1(t)− (h(s1)x1(t) + c(s1)) = s1 (x1(t))2 − c(s1)

Π2(t) = p2(t)x2(t)− (h(s2)x2(t) + c(s2)) = s2 (x2(t))2 − c(s2)

Prices of both qualities increase with the marginal cost of the foreign �rm.Prices of both �rms increase as protection becomes more intensive with the priceof the low quality/foreign product increasing more rapidly than the high qualityprice .

3.1.2 The socially optimal tari� :

We now focus on the host country. The government selects a tari� to maxi-mize domestic welfare de�ned as the sum of domestic consumers surplus, do-mestic �rm's pro�t, and tari� revenue. Indeed, when the emerging multinationalexports, setting a tari� allows an increase of the high quality/domestic �rm'spro�t and gives a tari� revenue to the government of the importing country.

When the multinational �rm exports, consumers' surplus at the optimum isgiven by :

CS(t) =p1(t)−p2(t)

s1−s2p2(t)

s2

(θs2 − p2(t))f(θ)dθ +θp1(t)−p2(t)

s1−s2

(θs1 − p1(t))f(θ)dθ

3The condition x2(t) > 0 de�nes a maximum value for t, denoted tmax =12

[(θ +

h(s1)s1

)s2 − 2d− 2h(s2)

], which is positive under the following assumption H1 :

θ +h(s1)

s1>

2d−2h(s2)s2

. This assumption guarantees that, in equilibrium, whatever the en-

try strategy adopted by the foreign �rm (export with or without tari�s or investment), it hasa strictly positive demand.

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that is, with a uniform distribution for which the density is 1

CS(t) =(p1(t)− p2(t)s1 − s2

− p2(t)s2

)[s22

(p1(t)− p2(t)s1 − s2

+p2(t)s2

)− p2(t)

]+(θ − p1(t)− p2(t)

s1 − s2

)[s12

(θ +

p1(t)− p2(t)s1 − s2

)− p1(t)

]where p1(t) and p2(t) are given respectively by (5) and (6).Tari� revenue is equal to the product of the tari� by the demand for the

low-quality good

TR(t) = t

[s1s2

θs2 − 2(t+ d+ h(s2))(4s1 − s2)

+h(s1)

(4s1 − s2)

]And the pro�t of the high quality/domestic �rm is

Π1(t) = s1

[θ(2s1 − s2) + t+ d+ h(s2)− 2h(s1)

(4s1 − s2)

]2− c(s1)

De�ning the host country welfare as

W (t) = CS(t) + TR(t) + Π1(t)

and maximizing with respect to t gives the following FOC (the second ordercondition being satis�ed ; −3s1/(4s1 − s2)s2 < 0)

s1(θs2 − 3t− d− h(s2))(4s1 − s2)s2

= 0

Such that the socially-optimal tari�, t∗, is equal to

t∗ =θs2 − (d+ h(s2))

3(7)

The optimal tari� is is independent of the domestic �rm characteristics. Itis proportional to the foreign �rm's quality level and depends positively on thesize of the market. And the higher the marginal cost (d+ h(s2)) of the foreign�rm is, the lower the optimal tari�.

In a Cournot setting with homogeneous product, Belderbos (1997a) esta-blishes that the socially optimal tari� depends on the di�erence between thedemand curve intercept and the marginal cost of the multinational. Otherwisestated, the optimal tari� is higher the greater the potential pro�ts of the mul-tinational. A similar result holds with di�erentiated product.

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3.2 The Bertrand case

3.2.1 Duopoly equilibrium : the export case

The pro�t functions of Firms 1 and 2 are

π1(p1, p2) = [p1 − h(s1)] (θ − p1 − p2

s1 − s2)− c(s1)

π2(p1, p2) = [p2 − h(s2)− t− d](p1 − p2

s1 − s2− p2

s2

)− c(s2)

Maximizing pro�ts with respect to price for both �rms and using the reactionfunctions, we obtain the following prices :

pb1(t) =2θs1(s1 − s2) + s1(d+ t+ 2h(s1) + h(s2))

(4s1 − s2)(8)

pb2(t) =θs2(s1 − s2) + 2s1(d+ t+ h(s2)) + s2h(s1)

(4s1 − s2)(9)

Because imposing a tari� on exports increases the marginal cost of the multi-national �rm, both �rms charge higher prices.

We obtain the following demand functions4 :

xb1(t) =2θs1(s1 − s2) + s1(d+ t− 2h(s1) + h(s2)) + h(s1)s2

(s1 − s2)(4s1 − s2)(10)

xb2(t) =s1s2

θ(s2s1 − s2)(s1 − s2)(4s1 − s2)

+s1s2

(d+ t+ h(s2))(s2 − 2s1)(s1 − s2)(4s1 − s2)

(11)

+s1h(s1)

(s1 − s2)(4s1 − s2)

Prices of both �rms increase with respect to free trade and the price of the lowquality/foreign product increases more rapidly than the price of the high qualityproduct as the tari� increases. The output of the high quality �rm increases andthe out put of the low quality/foreign frime decreases as t increases.

The equilibrium pro�ts then are

Πb1(t) =

(pb1(t)− h(s1)

)2s1 − s2

− c(s1) (12)

Πb2(t) =

s1s2

(pb2(t)− t− d− h(s2)

)2s1 − s2

− c(s2) (13)

4The condition xb2(t) > 0 de�nes a maximum value for t, denoted tbmax = h(s1)s2+θs2(s1−

s2) + (d + h(s2))(s2 − 2s1), which is positive under the following assumption H2 :h(s1)s2+θs2(s1 − s2) > (d + h(s2))(2s1 − s2). As in the Cournot case, this assumption gua-rantees that, in equilibrium, whatever the entry strategy adopted by the foreign �rm (exportwith or without tari�s or investment), it has a strictly positive demand.

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3.2.2 The socially optimal tari� :

As previously, the government selects a tari� to maximize domestic welfarede�ned as the sum of domestic consumers surplus, domestic �rm's pro�t andtari� revenue.

When the multinational �rm exports, consumers' surplus at the optimum isgiven by :

CSb(t) =(pb1(t)− pb2(t)s1 − s2

− pb2(t)s2

)[s22

(pb1(t)− pb2(t)s1 − s2

+pb2(t)s2

)− pb2(t)

]+(θ − pb1(t)− pb2(t)

s1 − s2

)[s12

(θ +

pb1(t)− pb2(t)s1 − s2

)− pb1(t)

]where pb1(t) and pb2(t) are given respectively by (8) and (9).Tari� revenue is equal to the product of the tari� by the demand for the

low-quality good

TR(t) = t

[s1s2

θ(s2s1 − s2)(s1 − s2)(4s1 − s2)

+s1s2

(d+ t+ h(s2))(s2 − 2s1)(s1 − s2)(4s1 − s2)

+s1h(s1)

(s1 − s2)(4s1 − s2)

]And the pro�t of the high quality/domestic �rm is

Πb1(t) =

(pb1(t)− h(s1)

)2s1 − s2

− c(s1)

Maximizing the host country welfare with respect to t gives the followingFOC (the second order condition being satis�ed ; s1(−3s1 +2s2)/(s1−s2)(4s1−s2)s2 < 0)

s1s2

(θs2 − d− t− h(s2))(s1 − s2)− t(2s1 − s2)(s1 − s2)(4s1 − s2)

= 0

Such that the socially-optimal tari�, t∗∗, is equal to

t∗∗ =θs2(s1 − s2)(3s1 − 2s2)

− (h(s2) + d)(s1 − s2)

(3s1 − 2s2)(14)

The optimal tari� is proportional to the degree of product di�erentiation,the foreign �rm's quality level and quality cost, and the size of the market.

3.3 On protection when quality matters

Considering a situation where the domestic government commits to an im-port tari� level before the �rms choose their output, several possibilities arise.

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The domestic government can choose the socially optimal tari� characterizedpreviously, which is the optimal tari� when the domestic market is a duopoly.But he could as well set a prohibitive tari� that is a tari� level such that thedomestic market remains a monopoly or a limit tari� that is a tari� level suchthat the foreign frim enters the domestic market and derives zero pro�t.

We �rst derive some considerations on the socially optimal tari�. We thencharacterize the limit tari� and the equilibrium outcome under the prohibitivetari�.

3.3.1 The socially optimal non-prohibitive tari�

Focusing on the alternative assumptions on costs of quality, one can establish,

Proposition 1 As the market internalizes the cost of quality, whatever the typeof competition, protection is higher under �xed costs than under variable costsof quality.

Proof. Direct when considering the optimal tari�s, t∗ and t∗∗, and assumingeither �xed costs of quality, h(s2) = 0, or variable costs of quality, h(s2) > 0.

This result is straighforward as variable costs are re�ected in market prices,whatever the type of competition, contrary to �xed costs which rather in�uencethe number of active �rms present in a market.

Now considering a particular type of quality costs and comparing the as-sumption of quantity versus price competition, we obtain that :

Proposition 2 : Whatever the nature of quality costs, either �xed or variable,protection is higher under Cournot competition than under Bertrand competi-tion.

Proof. Remind that, by assumption, s1 > s2. Under variable costs of quality,

one must compare t∗ = θs2−(d+h(s2))3 to t∗∗ = θs2(s1−s2)

(3s1−2s2)− (h(s2) + d) (s1−s2)

(3s1−2s2).

Under �xed quality costs, t∗ = θs2−d3 must be compared to t∗∗ = θs2(s1−s2)

(3s1−2s2)−

d(s1−s2)(3s1−2s2)

.

Product market competition matters. Indeed, with Bertand competition,�rms compete for the marginal consumer so that pro�tability is in�uenced bythe quality di�erential. The more di�erentiated the products, the less intenseis the competition and the higher the pro�ts of each �rm. While with Cournotcompetition, the pro�t of each �rm increases with its own quality and decreaseswith the quality of the other. For given qualities, competition appears to be moreintense under Cournot than under Bertrand. The welfare curve under Cournotcompetition is above the welfare curve under Bertrand. Protection favors thedomestic �rm and brings �scal return to the domestic governement but penalizes

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domestic consumers. In order to mitigate the impact of protection on consumerssurplus, the regulator chooses a lower tari� under Bertrand than under Cournot.

The results established in Propositions 1 and 2 are illustrated with a nu-merical example given in the following table. Considering possible parametersvalues : θ = 1; d = 0.05; s1 = 0.8; s2 = 0.7;h(s1) = 0.15;h(s2) = 0.1;G =0.005; c(s1) = s21

200 ; c(s2) = s22200 ;

type of quality costs optimal protection Cournot optimal protection Bertrand�xed costs 0.216667 0.065variable costs 0.1833 0.055

Tab. 1 � Proposition 1 and 2 : optimal protection when quality matters

3.3.2 The limit tari�

To characterize this tari�, we recourse to the zero pro�t condition for theforeign �rm. The limit tari� is the value of t, noted t, such that Π2(t) = 0

Under Cournot competition, this condition is given by

Π2(t) = s2 (x2(t))2−c(s2) = s2

(s1s2

θs2 − 2(t+ d+ h(s2))(4s1 − s2)

+h(s1)

(4s1 − s2)

)2

−c(s2) = 0

and the limit tari� writes

tc =

12s1

[(4s1 − s2)

√s2√c(s2) + s2h(s1) + s1

(θs2 − 2h(s2)

)]− d

The limit tari� is higher than the socially optimal tari�. And the higher isthe transport cost, the lower is the the limit tari�.

Under Bertrand competition, the condition is given by

Πb2(t) =

s1s2

(pb2(t)− t− d− h(s2)

)2s1 − s2

− c(s2)

which gives

tb =

1s1 (2s1 − s2)

[(4s1 − s2)

√s2√s1 (s1 − s2)

√c(s2) + s1

(s2(h(s1) + h(s2)− θs2

)+ s1

(θs2 − 2h(s2)

))]−d

The limit tari� is higher under Cournot than under Bertrand and it is higherunder variable cost than under �xed costs of quality.

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3.3.3 The prohibitive tari�

The situation with a prohibitive tari� is equivalent to the situation of au-tarky. The domestic/high quality �rm behaves as a monopoly on the domesticmarket. The consumer indi�erent between consuming one unit of high qualityand not consuming is identifed by the taste parameter θ10 = p1/s1. The de-mand for high quality consists in consumers with taste parameter higher thanθ10 ; x1(p1) = θ − p1

s1.

Considering that the monopolist chooses its quantity, the pro�ts are

π1(x1) = (s1(θ − x1)− h(s1))x1 − c(s1)

Maximizing with respect to x1, we obtain

xM1 =θ

2− h(s1)

2s1

pM1 = h(s1) +θs1 − h(s1)

2πM1 = s1(xM1 )2 − c(s1)

CSM = θpM1

s1

(θs1 − p1(t))f(θ)dθ =

(θs1 − h(s1)

)28s1

WM = πM1 + CSM =38

(θs1 − h(s1)

)2s1

− c(s1)

Observe that whatever the competitive setting and the nature of costs, whenquality is �xed, welfare under autarky is lower than the welfare under openeconomies(WM < W (0)). The opening of the economie allows some consumersexcluded from consumption in autarky to consume products of lower quality.As the domestic welfare in an increasing and concave function in t, the optimalcommercial policy, from the host country point of view would then be to set thesocially optimal tari�. But this is without considering potential tari� jumpingfrom the foreigh �rm.

We now turn to the analysis of the tari�-jumping FDI motivation.

4 FDI or exports ?

We remind ourselves that, when the emerging multinational chooses to in-vest, it saves on transport costs and tari� while it incurs an additional �xedcost G. Choosing between exporting and investing for the emerging multina-tional �rm thus results in a trade-o� between a reduced marginal cost and anadditional �xed cost G. Considering that the tari�-jumping motivation is a res-ponse to trade restraints, the decision to invest is directly in�uenced by the tari�level. We develop the idea that there exists a tari� value, the threshold tari�,that prevent the foreign �rm to export. We now characterize this threshold tari�under each competitive setting.

12

4.1 The threshold tari�

In a Cournot setting, the pro�t of Firm 2 in case of investment is :

πI2(x1, x2) = (θ − x1 − x2)s2x2 − h(s2)x2 − (c(s2) +G)

while Firm 1's pro�t is :

π1(x1, x2) = (θs1 − x1s1 − x2s2)x1 − h(s1)x1 − c(s1)

yielding the Nash equilibrium :

xI1 =θ (2s1 − s2)− 2h(s1) + h(s2)

4s1 − s2

xI2 =θs1 + h(s1)

4s1 − s2− 2h(s2)

4s1 − s2s1s2

With FDI, the output of the low quality �rm increases as it saves on transportcost and tari�, and the output of the high quality �rm decreases. Both pricesdecreases.

Firm 2's pro�t under FDI,

πI2 =

[(θs1 + h(s1)

)s2 − 2h(s2)s1

]2s2 (4s1 − s2)2

− (G+ c(s2)) (15)

must be compared to the pro�t under export,

Π2(t) = s2 (x2(t))2 − c(s2) =

(θs1s2 − 2s1(d+ t+ h(s2)) + h(s1)s2

)2s2 (4s1 − s2)2

− c(s2)

(16)

Choosing between exporting and investing for the emerging multinational�rm results in a trade-o� between a reduced marginal cost and an additional�xed cost G. A necessary and su�cient condition for the emerging multinational

to invest is that the pro�t realized under FDI is at least greater than the pro�tobtained under exports, πI2 ≥ Π2(t). This holds if

4(d+ t)s1[h(s1)s2 + s1(θs2 − d− t− 2h(s2))

]s2 (4s1 − s2)2

≥ G (17)

This condition, satis�ed as an equality, de�nes an interval for tari� values,[t1, t2], such that for all t ∈ [t1, t2], the emerging multinational invests. These

13

values are given in Appendix A. The length of this interval depends, amongother thing, on the quality costs and the �xed cost of direct investment.

In a Bertrand setting, the pro�t of the foreign �rm in case of investment is :

πb,I2 = (p2 − h(s2))(p1 − p2

s1 − s2− p2

s2

)− (G+ c(s2))

Maximizing both �rms' pro�ts with respect to prices yields the followingNash equilibrium

pb,I1 =s1[2θ(s1 − s2) + h(s2) + 2h(s1))

]4s1 − s2

pb,I2 =s2(θ(s1 − s2) + h(s1)) + 2s1h(s2)

4s1 − s2From free trade to FDI, prices of both �rms decreases. The high quality �rmproduces less while the low quality �rm increases its output.

Firm 2's pro�t under FDI,

πb,I2 =s1((h(s1) + θ(s1 − s2))s2 + h(s2)(2s1 − s2)2

(s1 − s2)s2 (4s1 − s2)2− (G+ c(s2))

must be compared to the pro�t under export,

Πb2(t) = s2 (x2(t))2 − c(s2)

=s1(s2(d+ t+ h(s1) + h(s2)− θs2) + s1(−2(d+ t)− 2h(s2) + θs2

))2

(s1 − s2)s2 (4s1 − s2)2− c(s2)

A necessary and su�cient condition for the emerging multinational to invest isthat the pro�t realized under FDI is at least greater than the pro�t obtainedunder exports, πb,I2 ≥ Πb

2(t). This holds if

G ≤(d+ t)s1(2s1 − s2)

[2s2

(θ(s1 − s2) + h(s1)

)− (2s1 − s2) (d+ t+ 2h(s2))

]s2(s1 − s2)(4s1 − s2)2

(18)

This condition, satis�ed as an equality, de�nes an interval for tari� values,[t1, t2], such that for all t ∈ [t1, t2], the emerging multinational invests. Thesevalues are given in Appendix A. The length of this interval depends, amongother thing, on the quality di�erential, the quality costs, the �xed cost of directinvestment.

Observe that, in a duopoly situation, not all values of this interval are ac-ceptable. Denoting t̃ ≡Min {t1, t2}, and taking into account the limit value fort de�ned by the limit tari�, t, the highest tari� that leaves a duopoly in themarket, one can establish the following proposition :

14

Proposition 3 In a oligopolistic situation, there exists a tari� threshold value,t̃, that depends on both assumptions on quality costs and competitive environ-ment, such that,For all t < t̃ the emerging multinational exports ;For all t > t > t̃, the emerging multinational invests.

Proof. Direct from the text.To penetrate the foreign market, the emerging multinational considers the

tari� threshold value, t̃, as well as the tari� indeed imposed by the government.The �rm proceeds to tari�-jump if the government sets a tari� at least equalto this threshold value, t̃. Observe that a limit tari� and hence forth a prohi-bitive tari� are circumvented. Although the prohibitive tari� can prevent theforeign �rm to enter the market by export, it does not prevent its enterring byinvestment.

Given the foreign �rm behavior with respect to the tari� level we have justdescribed, what type of trade policy should be chosen by the host country ?Does and when investment should be promoted ?

4.2 The host country trade policy

Let consider a situation where the socially optimal tari� is greater than thetari� threshold value, t̃, de�ned previously. With this tari� value, the emergingmultinational prefers to invest and we obtain the duopoly equilibrium underinvestment. From the host country point of view, what situation maximizes thedomestic welfare ? Free trade or FDI ?

In the Cournot duopoly equilibrium under investment, consumers surplus isreduced because of the prices increase but the high quality/domestic �rm pro�tincreases. With respect to the free-trade situation, one has a net positive e�ecton domestic welfare if and only if

∆W = WI −W (0) = (CSI − CS(0)) +(πI1 −Π1(0)

)> 0

After simplifying, one obtains the following expression

∆W =d [2h(s1)s2 − (d+ 2h(s2)) s1]

2s2 (4s1 − s2)

The sign of ∆W depends on the sign of the term in bracket so that it ispositive if

2h(s1)s1

>d

s2+

2h(s2)s2

(19)

In the Bertrand setting, FDI is preferred to the free-trade situation, from adomestic welfare point of view if and only if

∆W =(CSbI − CSb(0)

)+(πb,I1 −Πb

1(0))> 0

15

After simplifying, one obtains the following expression

∆W =ds1 [2h(s1)s2 − (d+ 2h(s2)s1]

2s2 (4s1 − s2) (s1 − s2)

The sign of ∆W depends on the sign of the term in bracket so that it is positiveif

2h(s1)s1

>d

s2+

2h(s2)s2

(20)

One has the following proposition

Proposition 4 From the host country point of view, whatever the competitivesetting, (i) when the cost of quality is �xed, free trade is preferred to FDI ; (ii)with variable costs of quality, FDI is preferred to free trade if and only if the

cost con�guration is such that 2h(s1)s1

> ds2

+ 2h(s2)s2

.

Proof. Direct from the text.In other words, the host country optimal tradel policy is independent of the

type of competition but depends on the assumption of quality costs and qualitylevels.

Whatever the type of competition, under �xed costs of quality, investmentalways entails a consumers surplus reduction that is more important than thedomestic �rm pro�t increase.

Finally, is the setting of the socially optimal tari� by the host country theoptimal trade policy ? No, if the socially optimal tari� is circumvented, thesecond best trade policy is to set a tari� slightly lower than the tari� thresholdvalue, t̃, decreases of pro�ts and consumers surplus generated by this trade policybeing more than o�set by the tari� revenue. This �second best� policy may alsobe preferred by the foreign �rm as well as the domestic �rm, as the numericalexample given in Appendix B illustrates.One has the following proposition

Proposition 5 From the host country point of view, whatever the competitivesetting, the �second best policy� is to set t̂ = t̃− ε (i) when the cost of quality is�xed ; (ii) with variable costs of quality, whenever d and G are such WI < W (t̃).

Proof. The domestic welfare is an increasing and concave function of t whichattains a maximum at t∗. When WI is lower than W (0) (the �xed cost case),the optimal commercial policy is to set the highest tari� that prevents tari�-jumping. When WI is higher than W (0) (the variable cost case) the optimalcommercial policy is identical as long as WI ≤W (t̃).

16

5 Conclusion

In this paper, we consider a situation where there are two �rms, an incumbentdomestic �rm o�ering a high-quality good and an emerging multinational o�e-ring a product of lower quality. With respect to protection, we establish thatthe optimal tari� depends on the costs of quality. As the market internalizes thecosts of quality, whatever the type of competition, protection is higher under�xed costs than under variable costs of quality. Whatever the nature of qualitycosts, either �xed or variable, protection is higher under Cournot competitionthan under Bertrand competition.

With respect to the emerging multinational' incentive to invest rather thanexport (tari�-jumping FDI), the decision relies on the comparison between va-riable costs and �xed costs : investing abroad increases �xed costs while expor-ting increases variable costs. We show that in a oligopolistic situation, thereexists a tari� threshold value under which the multinational exports and abovewhich the multinational invests. In order to penetrate the foreign market, theemerging multinational considers the tari� threshold value as well as the tari�imposed by the host country. The multinational proceeds to tari�-jump if thehost country sets a tari� at least equal to the threshold value. This thresholdvalue is in�ucenced by both types of assumptions.

We then derive some conclusions on the host country optimal trade policy.In case the socially optimal tari� is circumvented, setting a tari� slightly lowerthan the tari� threshold value may be welfare improving. Such a second bestpolicy may also be preferred by the foreigh �rm as well as the domestic �rm.

Finally, these results are derived with �xed qualities. Our assumption thatthe foreign �rm produces low quality is consistent with the results established forinstance by Herguera et al.(2002). Further research should consider the impactof potential tari� jumping on investment in quality.

17

Appendix A

In the Cournot setting, the interval of tari� values is,

tc1 =1

2s1(−2ds21 − 2h(s2)s21 + h(s1)s1s2 + θs21s2 −

s1(4h(s2)2s21 − 4h(s2)h(s1)s1s2 − 16Gs21s2

−4θh(s2)s21s2 + h(s1)2s22 + 8Gs1s22 + 2θh(s1)s1s22 + θ2s21s

22 −Gs32)1/2)

tc2 =1

2s1(−2ds21 − 2h(s2)s21 + h(s1)s1s2 + θs21s2 +

s(4h(s2)2s21 − 4h(s2)h(s1)s1s2 − 16Gs21s2

−4θh(s2)s21s2 + h(s1)2s22 + 8Gs1s22 + 2θh(s1)s1s22 + θ2s21s

22 −Gs32)1/2

In the Bertrand setting, one has,

tb1 =1

√s1 (2s1 − s2)

(√s1(s2(d+ h(s1) + h(s2)− θs2) + s1(−2(d+ h(s2) + θs2)

−((−2h(s2)s1(h(s1) + θ(s1 − s2))(2s1 − s2)s2+h(s2)2s1(−2s1 + s2)2 + s2(−16Gs31 + s1(24Gs1 + (h(s1) + θs1)2)s2

−s1(9G+ 2θ(h(s1) + θs1)) + (G+ θ2s1)s32)))1/2)

tb1 =1

√s1 (2s1 − s2)

(√s1(s2(d+ h(s1) + h(s2)− θs2) + s1(−2(d+ h(s2) + θs2)

+((−2h(s2)s1(h(s1) + θ(s1 − s2))(2s1 − s2)s2+h(s2)2s1(−2s1 + s2)2 + s2(−16Gs31 + s1(24Gs1 + (h(s1) + θs1)2)s2

−s1(9G+ 2θ(h(s1) + θs1)) + (G+ θ2s1)s32))1/2)

18

Autarky vs Free trade

Cournot Situation

Parameters values : θ = 5; d = 0.1; s1 = 3.69; s2 = 2.93;Bertrand situation

Parameters values : θ = 5; d = 0.1; s1 = 4.10; s2 = 1.99;

Welfare under autarky Welfare under free-tradeCournot �xed costs 11.5313 24.9302variable costs 4.59129 12.6914Bertrand, �xed costs 12.8125 43.7457variable costs 4.46003 15.8401

19

Appendix B

A numerical example

The alternative situations are described in the following tables.

Cournot Situation

Parameters values : θ = 5; d = 0.1; s1 = 3.69; s2 = 2.93;Bertrand situation

Parameters values : θ = 5; d = 0.1; s1 = 4.10; s2 = 1.99;

Trade policy Domestic �rm pro�t foreign �rm pro�t Welfare host countryfree trade ; t = 0 0.072 0.0412857 0.179643t1 = 0.146588 0.102895 0.00829143 0.201765t∗ = 0.183333 0.111502 0.00396254 0.20269FDI 0.06272 0.00829143 0.179786

Tab. 2 � Cournot situation with variable costs

Parameters values : θ = 1; d = 0.01; s1 = 0.8; s2 = 0.7; c(s1) = s21200 ; c(s2) =

s22200 ;G = 0.005

Trade policy Domestic �rm pro�t Foreign �rm pro�t Welfare host countryfree trade ; t = 0 0.11232 0.0502129 0.269371t1 = 0.107514 0.139947 0.01923 0.293392t∗ = 0.216667 0.171022 0.00161349 0.301562FDI 0.10048 0.01923 0.2688

Tab. 3 � Cournot situation with �xed costs

20

Bertrand situation

Parameters values : θ = 1; d = 0.05; s1 = 0.8; s2 = 0.7;h(s1) = 0.3;h(s2) =0.1;G = 0.005

Trade policy Domestic �rm pro�t Foreign �rm pro�t Welfare host countryfree trade ; t = 0 0.0259003 0.0234411 0.143635t1 = 0.00720728 0.0271705 0.0214106 0.145228t∗ = 0.0835714 0.0424956 0.00554654 0.153292FDI 0.0241884 0.0214106 0.144938

Tab. 4 � Bertand situation with variable costs

Parameters values : θ = 1; d = 0.01; s1 = 0.8; s2 = 0.5; c(s1) = s21200 ; c(s2) =

s22200 ;G = 0.005

Trade policy Domestic �rm pro�t Foreign �rm pro�t Welfare host countryfree trade ; t = 0 0.105691 0.0128852 0.352435t1 = 0.0125796 0.110228 0.0102109 0.355869t∗ = 0.105 0.146404 −0.000845978 0.367679FDI 0.10215 0.0102109 0.352356

Tab. 5 � Bertrand situation with �xed costs

21

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